Are cars deadly weapons? Yes, they can be.
Are baseball bats deadly weapons? Yes, they can be.
Are screw drivers bats deadly weapons? Yes, they can be.
Are fists deadly weapons? Yes, they can be.
So , if police had the 'right' to investigate everyone carrying something that could be used as a deadly weapon, then you have a major problem.
On top of that, during hunting season all across the US it's common practice to carry a firearm. While driving around on any given shotgun season day in my area, I'll see no less than 50 to 100 individuals carrying around shotguns or handguns. Hunting and firearms are just part of the lifestyle in the US, just like it is in Switzerland.
The problem is, many people in the US now grow up in heavily urban areas and see firearms as only good for killing people, and nothing else. Because of this they feel that everyone who owns or carries a gun must be up to no good and therefor attempt to use the law to suppress people who exercise their right to carry a firearm.